1. Field of the Invention
The present invention relates to a control system for controlling the torque of an induction motor by means of the current and frequency thereof.
2. Prior Art
FIG. 1 shows a conventional control system for an induction motor. In the drawing, there are shown an induction motor 1, a rotation detector 2 for detecting the rotation speed of the induction motor 1, a current detector 3 for detecting the primary current of the induction motor 1, a variable frequency-power converter unit 4 for driving the induction motor 1 by means of variable frequencies, a torque command generator 5 for generating a torque command T.sub.M *, a torque-current component command generator 6 for receiving the torque command T.sub.M * and generating a torque-current component command I.sub.96 * having a predetermined correspondence therebetween, a flux command generator 7 for generating a secondary magnetic-flux command .PHI..sub.2 *, an excitation-current component command generator 8 for receiving the secondary flux command .PHI..sub.2 * and generating an excitation-current component command I.sub.E * having a predetermined correspondence therebetween, a current-vector arithmetic circuit 9 for receiving the torque-current component command I.sub..tau. * and the excitation-current component command I.sub.E * and for generating a primary-current amplitude command .vertline.I.sub.l *.vertline., a phase command .theta..sub.96 * and a slip angle frequency command .omega..sub.s *, as computed below, which are applied to the induction motor 1, a current command generating circuit 10 for receiving the output signal from the current-vector arithmetic circuit 9 and the rotation speed .omega..sub.r from the rotation detector 2 and for computing primary-current commands which are applied to the induction motor 1, and a current control circuit 11 for receiving the output signals from the current command generating circuit 10 and the output signal from the current detector 3 and for generating control signals applied to the variable frequencypower converter 4.
The current-vector arithmetic circuit 9 comprising circuits 91 to 93 performs the following operation: ##EQU1## EQU .theta..sub..tau. *=tan.sup.-1 (I.sub..tau. */I.sub.E *) (2) ##EQU2## where T.sub.2 =L.sub.2 /R.sub.2, R.sub.2 and L.sub.2 are a secondary winding resistance and a secondary winding inductance, respectively, of the induction motor 1.
In order to generate the primary current commands i.sub.us * and i.sub.vs * which are respectively applied to the u phase winding and the v phase winding of the induction motor 1, the current command generating circuit 10 performs the following operation: ##EQU3## where .omega..sub.o =.omega..sub.r +.omega..sub.s * (5)
In the current control circuit 11, the primary current commands i.sub.us * and i.sub.vs * are compared with the actual primary currents i.sub.us and i.sub.vs, respectively, from the primary current detectors 3 so that the waveforms of the current commands are correspondingly coincident with those of the actual primary currents, and then the control signals are operated for application to the variable frequency-power converter 4.
At this time, with respect to the primary current flow through the w phase winding, the primary current commands i.sub.ws * and i.sub.ws can also be controlled is the same manner as the primary currents i.sub.us and i.sub.vs, and be computed by the following: EQU i.sub.ws *=-(i.sub.us *+i.sub.vs *) (6) EQU i.sub.ws =-(i.sub.us +i.sub.vs) (7)
In general, a control system in which the primary current commands i.sub.us *, i.sub.vs * and i.sub.ws * are computed by the formulas (1) through (6) as described above and the actual primary currents i.sub.us, i.sub.vs and i.sub.ws are controlled to coincide with the corresponding commands may be called "a vector control method". In this method, assuming that the excitation-current component command I.sub.E * is fixed, it is known that the torque of the induction motor 1 changes in proporton to the torque-current component command I.sub..tau. * and the variable speed control of the induction motor can therefore be effected in a stable manner and such as to provide a relatively high speed response.
According to this control system, it is noted that, as understood from the formula (3), the values of the secondary winding resistance R.sub.2 and the secondary winding inductance L.sub.2 which are the numerical constants of the induction motor 1 are required to operate the primary current command. Since the secondary winding resistance R.sub.2 is under the influence of temperature, if any one of the values R.sub.2, T.sub.2 =L.sub.2 /R.sub.2 in the current vector arithmetic circuit 9 is corrected by a certain means, the linearity of a torque-to-torque current component command I.sub..tau. * characteristic may be damaged and furthermore it may be impossible to control the torque or secondary flux of the induction motor 1 in response to the respective commands.
A circuit which, for example, compensates for the change in temperature of the secondary winding resistance R.sub.2 is shown in FIG. 2. The detailed compensation circuit is disclosed in the publication "IEEE Trsns. IA Vol. IA-16, No. 2, pp 173-178, 1980".
In FIG. 2, there are shown a first power arithmetic circuit 12 for receiving the primary voltages .upsilon..sub.us and .upsilon..sub.vs and the primary currents i.sub.us and i.sub.vs of the induction motor 1 and for detecting an electric energy F.sub.o, as computed below, which is associated with a reactive power generated in the induction motor 1, a second power arithmetic circuit 13 for receiving the secondary flux command .PHI..sub.2 *, the torque-current component command I.sub..tau. *, the slip angle frequency command .omega..sub.s * and the rotation speed .omega..sub.r of the induction motor and for computing an electric energy F.sub.o *, as described below, which corresponds to the electric energy F.sub.o, and a compensation circuit 14.
The operation formulas and the compensation method of the electric energies F.sub.o and F.sub.o * will next be explained. Note that the numerical constants in the control circuits, such as the current-vector arithmetic circuit 9, of the induction motor 1 will be marked with asterisks (for example, R.sub.2 *).
As is known by those skilled in the art, the voltage equations of the stator or primary side of the induction motor on a d-q axis coordinate system are given by ##EQU4## where .upsilon..sub.ds and .upsilon..sub.qs are the d axis and q axis components, respectively, of the primary voltage;
i.sub.ds and i.sub.qs are the d axis and q axis components, respectively, of the primary current; PA1 .PHI..sub.2d and .PHI..sub.2q are the d axis and q axis components, respectively, of the secondary flux; PA1 P=d/dt is a differential operator; and PA1 R.sub.1, L.sub.1, M and L.sub.2 are the primary winding resistance, the primary winding inductance, the primary-secondary winding mutual inductance and the secondary winding inductance, respectively, of the induction motor.
In addition, a leakage coefficient .sigma. is given by ##EQU5##
Using the formula (8), the reactive power Q is represented by the following: ##EQU6##
On the other hand, as is well known, if the primary currents of the induction motor are controlled in accordance with the formulas (1) through (6) then the following can be obtained: ##EQU7## where i.sub.ds *, i.sub.qs *, .PHI..sub.2d * and .PHI..sub.2q * are the commands i.sub.ds, i.sub.qs, .PHI..sub.2d and .PHI..sub.2q, respectively, and .omega..sub.o is given by the formula (5).
Note that the formula (11) can be obtained by cancelling the primary current commands i.sub.us * and i.sub.vs * from the formulas (1) through (4) and the formula (16) as described below.
Using the formulas (11) and (12), the following can be obtained: ##EQU8##
By the formula (10), a formula corresonding to the formula (13) is as follows: ##EQU9##
Thus, the formula (14) is not affected by the change in temperature of the secondary winding resistance R.sub.2 and can be easily computed by using the primary voltages and the primary currents of the induction motor, because it does not include the resistance R.sub.2.
Alternatively, although the formula (13) does not include the secondary winding resistance R.sub.2 per se, all of I.sub.E *, I.sub..tau. * and .PHI..sub.2 * denote the command values. This means that, if the value R.sub.2 * does not coincide with the actual value R.sub.2, the excitation current I.sub.E, the torque current I.sub..tau. and the secondary flux .PHI..sub.2 do not coincide with the respective commands.
It is understood, therefore, that there is a deviation between the value computed by the formula (13) and the value computed by the formula (14). Conclusively, the command value R.sub.2 * or T.sub.2 * in the current-vector arithmetic circuit 9 can be corrected so that the deviation becomes zero. In FIG. 2, the value T.sub.2 * is corrected on the basis of the principle above.
Now, as is known, the relationship among the d axis and q axis components .upsilon..sub.ds and .upsilon..sub.qs of the primary voltage, the primary volatges .upsilon..sub.us and .upsilon..sub.vs, and the d axis and q axis components i.sub.ds and i.sub.vs of the primary current is given by ##EQU10##
By inserting the formulas (15) and (16) into the right member of the formula (14) and cancelling the d axis and q axis components .upsilon..sub.ds and .upsilon..sub.qs of the primary voltage and the d axis and q axis components i.sub.ds and i.sub.qs of the primary current, the operation formula of the electric energy F.sub.o is calculated as follows: ##EQU11##
Also, according to the right member of the formula (13), the operation formula of the electric energy F.sub.o * is given by ##EQU12##
The operation of the compensation circuit shown in FIG. 2 will next be explained.
First, as the output signals from the first and second power arithmetic circuits 12 and 13, the electric energies F.sub.o and F.sub.o * are obtained by computing each of the formulas (17) and (18).
Second, a subtractor 141 outputs a deviation .DELTA.F.sub.o between the electric energies F.sub.o * and F.sub.o, which is integrated by an integrator 142 to obtain an amount of correction .DELTA.T.sub.2 * for a numerical constant setting value T.sub.2 *. The amount of correction .DELTA.T.sub.2 * and a preset amount T.sub.20 * for the value T.sub.2 * are added by an adder 143 to thereby obtain a corrected value T.sub.2 *.
As the result, in FIG. 1, the value T.sub.2 * is corrected in the current-vector arithmetic circuit 9 and therefore the linearity between the torque-current component command I.sub..tau. * and the torque can be maintained, even if any change of the secondary winding resistance R.sub.2 is caused by the change in temperature.
As the conventional control system of the induction motor is constructed as described above, under the operating condition, the value of the secondary winding resistance in the control circuit of the induction motor has been compensated for with respect to the change in temperature thereof and the command values such as the excitation-current component command I.sub.E * or the torque-current component command I.sub..tau. * have been utilized to compute the electric energy F.sub.o * used in the compensation circuit.
Due to the deviation or difference between the actual and command values of the primary current, which is caused by a characteristic of the current control circuit wherein the actual values i.sub.us, i.sub.vs and i.sub.ws of the primary currents are controlled to coincide with the respective commands, or the limitation of the variable frequency-power converter, such as the withstand current or the withstand voltage, if the control system is saturated under a certain operating condition then it may be impossible to apply the excitation-current component I.sub.E and the torque-current component I.sub..tau. to the induction motor in response to the corresponding commands, even if the value of the secondary winding resistance is properly corrected.
In this case, a problem has been experienced wherein any deviation that occurs between the electric energies F.sub.o * and F.sub.o causes the compensation circuit to provide a wrong correction, despite the properly corrected value of the secondary winding resistance.